both are great choices, the .243 and 7mm-08

I think the 7-08 is only gonna continue to get more popular.

The .308 is a hugely popular option if you're really worried about the 7mm08.

I think of your two choices, the 7mm08 would be more versatile than the .243, but in reality you're probably not going to use either on elk, we're talking varmints-deer size game here and either would do that job well.